LMFDB - Embedded newform 9680.2.a.cb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9680,2,Mod(1,9680)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9680, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9680.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9680 = 2^{4} \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9680.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$77.2951891566$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.86620$ of defining polynomial
Character	$\chi$	$=$	9680.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.86620 q^{3} -1.00000 q^{5} +3.38350 q^{7} +5.21509 q^{9} +O(q^{10})$	$q-2.86620 q^{3} -1.00000 q^{5} +3.38350 q^{7} +5.21509 q^{9} +1.48270 q^{13} +2.86620 q^{15} -3.73240 q^{17} +3.21509 q^{19} -9.69779 q^{21} +2.51730 q^{23} +1.00000 q^{25} -6.34889 q^{27} +4.69779 q^{29} -9.21509 q^{31} -3.38350 q^{35} -2.69779 q^{37} -4.24970 q^{39} +4.55191 q^{41} -5.38350 q^{43} -5.21509 q^{45} +10.5294 q^{47} +4.44809 q^{49} +10.6978 q^{51} -2.51730 q^{53} -9.21509 q^{57} -11.9129 q^{59} -13.6799 q^{61} +17.6453 q^{63} -1.48270 q^{65} -7.83159 q^{67} -7.21509 q^{69} -2.51730 q^{71} -2.96539 q^{73} -2.86620 q^{75} -6.76700 q^{79} +2.55191 q^{81} -7.55191 q^{83} +3.73240 q^{85} -13.4648 q^{87} +10.8016 q^{89} +5.01671 q^{91} +26.4123 q^{93} -3.21509 q^{95} +11.0167 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{3} - 3 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) $ 3 * q - q^3 - 3 * q^5 + q^7 + 2 * q^9	$ 3 q - q^{3} - 3 q^{5} + q^{7} + 2 q^{9} + 6 q^{13} + q^{15} + 4 q^{17} - 4 q^{19} - 17 q^{21} + 6 q^{23} + 3 q^{25} - 13 q^{27} + 2 q^{29} - 14 q^{31} - q^{35} + 4 q^{37} + 4 q^{39} + 9 q^{41} - 7 q^{43} - 2 q^{45} + 15 q^{47} + 18 q^{49} + 20 q^{51} - 6 q^{53} - 14 q^{57} - 10 q^{59} + 3 q^{61} + 12 q^{63} - 6 q^{65} - 19 q^{67} - 8 q^{69} - 6 q^{71} - 12 q^{73} - q^{75} - 2 q^{79} + 3 q^{81} - 18 q^{83} - 4 q^{85} - 10 q^{87} + 11 q^{89} - 20 q^{91} + 20 q^{93} + 4 q^{95} - 2 q^{97}+O(q^{100}) $ 3 * q - q^3 - 3 * q^5 + q^7 + 2 * q^9 + 6 * q^13 + q^15 + 4 * q^17 - 4 * q^19 - 17 * q^21 + 6 * q^23 + 3 * q^25 - 13 * q^27 + 2 * q^29 - 14 * q^31 - q^35 + 4 * q^37 + 4 * q^39 + 9 * q^41 - 7 * q^43 - 2 * q^45 + 15 * q^47 + 18 * q^49 + 20 * q^51 - 6 * q^53 - 14 * q^57 - 10 * q^59 + 3 * q^61 + 12 * q^63 - 6 * q^65 - 19 * q^67 - 8 * q^69 - 6 * q^71 - 12 * q^73 - q^75 - 2 * q^79 + 3 * q^81 - 18 * q^83 - 4 * q^85 - 10 * q^87 + 11 * q^89 - 20 * q^91 + 20 * q^93 + 4 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	−2.86620	−1.65480	−0.827400	−	0.561613i	$-0.810181\pi$
$3$	−2.86620	−1.65480	−0.827400	+	0.561613i	$0.810181\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	3.38350	1.27884	0.639422	−	0.768856i	$-0.279174\pi$
$7$	3.38350	1.27884	0.639422	+	0.768856i	$0.279174\pi$
$8$	0	0
$9$	5.21509	1.73836
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	1.48270	0.411226	0.205613	−	0.978633i	$-0.434081\pi$
$13$	1.48270	0.411226	0.205613	+	0.978633i	$0.434081\pi$
$14$	0	0
$15$	2.86620	0.740049
$16$	0	0
$17$	−3.73240	−0.905239	−0.452620	−	0.891704i	$-0.649510\pi$
$17$	−3.73240	−0.905239	−0.452620	+	0.891704i	$0.649510\pi$
$18$	0	0
$19$	3.21509	0.737593	0.368796	−	0.929510i	$-0.379770\pi$
$19$	3.21509	0.737593	0.368796	+	0.929510i	$0.379770\pi$
$20$	0	0
$21$	−9.69779	−2.11623
$22$	0	0
$23$	2.51730	0.524894	0.262447	−	0.964946i	$-0.415470\pi$
$23$	2.51730	0.524894	0.262447	+	0.964946i	$0.415470\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−6.34889	−1.22185
$28$	0	0
$29$	4.69779	0.872357	0.436179	−	0.899860i	$-0.356332\pi$
$29$	4.69779	0.872357	0.436179	+	0.899860i	$0.356332\pi$
$30$	0	0
$31$	−9.21509	−1.65508	−0.827540	−	0.561407i	$-0.810260\pi$
$31$	−9.21509	−1.65508	−0.827540	+	0.561407i	$0.810260\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−3.38350	−0.571916
$36$	0	0
$37$	−2.69779	−0.443514	−0.221757	−	0.975102i	$-0.571179\pi$
$37$	−2.69779	−0.443514	−0.221757	+	0.975102i	$0.571179\pi$
$38$	0	0
$39$	−4.24970	−0.680497
$40$	0	0
$41$	4.55191	0.710889	0.355445	−	0.934697i	$-0.384329\pi$
$41$	4.55191	0.710889	0.355445	+	0.934697i	$0.384329\pi$
$42$	0	0
$43$	−5.38350	−0.820976	−0.410488	−	0.911866i	$-0.634642\pi$
$43$	−5.38350	−0.820976	−0.410488	+	0.911866i	$0.634642\pi$
$44$	0	0
$45$	−5.21509	−0.777420
$46$	0	0
$47$	10.5294	1.53587	0.767934	−	0.640529i	$-0.221285\pi$
$47$	10.5294	1.53587	0.767934	+	0.640529i	$0.221285\pi$
$48$	0	0
$49$	4.44809	0.635441
$50$	0	0
$51$	10.6978	1.49799
$52$	0	0
$53$	−2.51730	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$53$	−2.51730	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−9.21509	−1.22057
$58$	0	0
$59$	−11.9129	−1.55092	−0.775462	−	0.631394i	$-0.782483\pi$
$59$	−11.9129	−1.55092	−0.775462	+	0.631394i	$0.782483\pi$
$60$	0	0
$61$	−13.6799	−1.75153	−0.875765	−	0.482738i	$-0.839642\pi$
$61$	−13.6799	−1.75153	−0.875765	+	0.482738i	$0.839642\pi$
$62$	0	0
$63$	17.6453	2.22310
$64$	0	0
$65$	−1.48270	−0.183906
$66$	0	0
$67$	−7.83159	−0.956781	−0.478391	−	0.878147i	$-0.658780\pi$
$67$	−7.83159	−0.956781	−0.478391	+	0.878147i	$0.658780\pi$
$68$	0	0
$69$	−7.21509	−0.868595
$70$	0	0
$71$	−2.51730	−0.298749	−0.149375	−	0.988781i	$-0.547726\pi$
$71$	−2.51730	−0.298749	−0.149375	+	0.988781i	$0.547726\pi$
$72$	0	0
$73$	−2.96539	−0.347073	−0.173536	−	0.984827i	$-0.555519\pi$
$73$	−2.96539	−0.347073	−0.173536	+	0.984827i	$0.555519\pi$
$74$	0	0
$75$	−2.86620	−0.330960
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−6.76700	−0.761348	−0.380674	−	0.924709i	$-0.624308\pi$
$79$	−6.76700	−0.761348	−0.380674	+	0.924709i	$0.624308\pi$
$80$	0	0
$81$	2.55191	0.283546
$82$	0	0
$83$	−7.55191	−0.828930	−0.414465	−	0.910065i	$-0.636031\pi$
$83$	−7.55191	−0.828930	−0.414465	+	0.910065i	$0.636031\pi$
$84$	0	0
$85$	3.73240	0.404835
$86$	0	0
$87$	−13.4648	−1.44358
$88$	0	0
$89$	10.8016	1.14497	0.572484	−	0.819916i	$-0.305980\pi$
$89$	10.8016	1.14497	0.572484	+	0.819916i	$0.305980\pi$
$90$	0	0
$91$	5.01671	0.525894
$92$	0	0
$93$	26.4123	2.73883
$94$	0	0
$95$	−3.21509	−0.329862
$96$	0	0
$97$	11.0167	1.11858	0.559288	−	0.828973i	$-0.311074\pi$
$97$	11.0167	1.11858	0.559288	+	0.828973i	$0.311074\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−12.7324	−1.26692	−0.633460	−	0.773775i	$-0.718366\pi$
$101$	−12.7324	−1.26692	−0.633460	+	0.773775i	$0.718366\pi$
$102$	0	0
$103$	18.3431	1.80740	0.903698	−	0.428170i	$-0.140842\pi$
$103$	18.3431	1.80740	0.903698	+	0.428170i	$0.140842\pi$
$104$	0	0
$105$	9.69779	0.946407
$106$	0	0
$107$	−7.13380	−0.689651	−0.344825	−	0.938667i	$-0.612062\pi$
$107$	−7.13380	−0.689651	−0.344825	+	0.938667i	$0.612062\pi$
$108$	0	0
$109$	4.14588	0.397103	0.198551	−	0.980090i	$-0.436376\pi$
$109$	4.14588	0.397103	0.198551	+	0.980090i	$0.436376\pi$
$110$	0	0
$111$	7.73240	0.733927
$112$	0	0
$113$	1.46479	0.137796	0.0688981	−	0.997624i	$-0.478052\pi$
$113$	1.46479	0.137796	0.0688981	+	0.997624i	$0.478052\pi$
$114$	0	0
$115$	−2.51730	−0.234740
$116$	0	0
$117$	7.73240	0.714860
$118$	0	0
$119$	−12.6286	−1.15766
$120$	0	0
$121$	0	0
$122$	0	0
$123$	−13.0467	−1.17638
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−11.2964	−1.00239	−0.501196	−	0.865334i	$-0.667106\pi$
$127$	−11.2964	−1.00239	−0.501196	+	0.865334i	$0.667106\pi$
$128$	0	0
$129$	15.4302	1.35855
$130$	0	0
$131$	14.6799	1.28259	0.641294	−	0.767295i	$-0.278398\pi$
$131$	14.6799	1.28259	0.641294	+	0.767295i	$0.278398\pi$
$132$	0	0
$133$	10.8783	0.943266
$134$	0	0
$135$	6.34889	0.546426
$136$	0	0
$137$	−15.6453	−1.33667	−0.668333	−	0.743862i	$-0.732992\pi$
$137$	−15.6453	−1.33667	−0.668333	+	0.743862i	$0.732992\pi$
$138$	0	0
$139$	−7.64528	−0.648464	−0.324232	−	0.945978i	$-0.605106\pi$
$139$	−7.64528	−0.648464	−0.324232	+	0.945978i	$0.605106\pi$
$140$	0	0
$141$	−30.1793	−2.54155
$142$	0	0
$143$	0	0
$144$	0	0
$145$	−4.69779	−0.390130
$146$	0	0
$147$	−12.7491	−1.05153
$148$	0	0
$149$	6.48270	0.531083	0.265542	−	0.964099i	$-0.414449\pi$
$149$	6.48270	0.531083	0.265542	+	0.964099i	$0.414449\pi$
$150$	0	0
$151$	−10.8783	−0.885261	−0.442631	−	0.896704i	$-0.645955\pi$
$151$	−10.8783	−0.885261	−0.442631	+	0.896704i	$0.645955\pi$
$152$	0	0
$153$	−19.4648	−1.57364
$154$	0	0
$155$	9.21509	0.740174
$156$	0	0
$157$	10.4302	0.832419	0.416210	−	0.909269i	$-0.363358\pi$
$157$	10.4302	0.832419	0.416210	+	0.909269i	$0.363358\pi$
$158$	0	0
$159$	7.21509	0.572194
$160$	0	0
$161$	8.51730	0.671258
$162$	0	0
$163$	10.2439	0.802362	0.401181	−	0.915999i	$-0.368600\pi$
$163$	10.2439	0.802362	0.401181	+	0.915999i	$0.368600\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	1.04668	0.0809947	0.0404974	−	0.999180i	$-0.487106\pi$
$167$	1.04668	0.0809947	0.0404974	+	0.999180i	$0.487106\pi$
$168$	0	0
$169$	−10.8016	−0.830893
$170$	0	0
$171$	16.7670	1.28220
$172$	0	0
$173$	11.9129	0.905720	0.452860	−	0.891582i	$-0.350404\pi$
$173$	11.9129	0.905720	0.452860	+	0.891582i	$0.350404\pi$
$174$	0	0
$175$	3.38350	0.255769
$176$	0	0
$177$	34.1447	2.56647
$178$	0	0
$179$	3.39558	0.253797	0.126899	−	0.991916i	$-0.459498\pi$
$179$	3.39558	0.253797	0.126899	+	0.991916i	$0.459498\pi$
$180$	0	0
$181$	−5.69779	−0.423513	−0.211757	−	0.977322i	$-0.567918\pi$
$181$	−5.69779	−0.423513	−0.211757	+	0.977322i	$0.567918\pi$
$182$	0	0
$183$	39.2093	2.89843
$184$	0	0
$185$	2.69779	0.198345
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−21.4815	−1.56255
$190$	0	0
$191$	9.01671	0.652426	0.326213	−	0.945296i	$-0.394227\pi$
$191$	9.01671	0.652426	0.326213	+	0.945296i	$0.394227\pi$
$192$	0	0
$193$	26.2318	1.88821	0.944103	−	0.329650i	$-0.106931\pi$
$193$	26.2318	1.88821	0.944103	+	0.329650i	$0.106931\pi$
$194$	0	0
$195$	4.24970	0.304327
$196$	0	0
$197$	−16.6978	−1.18967	−0.594834	−	0.803849i	$-0.702782\pi$
$197$	−16.6978	−1.18967	−0.594834	+	0.803849i	$0.702782\pi$
$198$	0	0
$199$	16.7912	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$199$	16.7912	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$200$	0	0
$201$	22.4469	1.58328
$202$	0	0
$203$	15.8950	1.11561
$204$	0	0
$205$	−4.55191	−0.317919
$206$	0	0
$207$	13.1280	0.912457
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−7.64528	−0.526323	−0.263161	−	0.964752i	$-0.584765\pi$
$211$	−7.64528	−0.526323	−0.263161	+	0.964752i	$0.584765\pi$
$212$	0	0
$213$	7.21509	0.494370
$214$	0	0
$215$	5.38350	0.367152
$216$	0	0
$217$	−31.1793	−2.11659
$218$	0	0
$219$	8.49940	0.574336
$220$	0	0
$221$	−5.53401	−0.372258
$222$	0	0
$223$	3.78954	0.253766	0.126883	−	0.991918i	$-0.459503\pi$
$223$	3.78954	0.253766	0.126883	+	0.991918i	$0.459503\pi$
$224$	0	0
$225$	5.21509	0.347673
$226$	0	0
$227$	19.5461	1.29732	0.648660	−	0.761079i	$-0.275330\pi$
$227$	19.5461	1.29732	0.648660	+	0.761079i	$0.275330\pi$
$228$	0	0
$229$	5.16258	0.341153	0.170576	−	0.985344i	$-0.445437\pi$
$229$	5.16258	0.341153	0.170576	+	0.985344i	$0.445437\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	6.24970	0.409431	0.204716	−	0.978821i	$-0.434373\pi$
$233$	6.24970	0.409431	0.204716	+	0.978821i	$0.434373\pi$
$234$	0	0
$235$	−10.5294	−0.686861
$236$	0	0
$237$	19.3956	1.25988
$238$	0	0
$239$	−4.61067	−0.298239	−0.149120	−	0.988819i	$-0.547644\pi$
$239$	−4.61067	−0.298239	−0.149120	+	0.988819i	$0.547644\pi$
$240$	0	0
$241$	7.87827	0.507484	0.253742	−	0.967272i	$-0.418339\pi$
$241$	7.87827	0.507484	0.253742	+	0.967272i	$0.418339\pi$
$242$	0	0
$243$	11.7324	0.752634
$244$	0	0
$245$	−4.44809	−0.284178
$246$	0	0
$247$	4.76700	0.303317
$248$	0	0
$249$	21.6453	1.37171
$250$	0	0
$251$	−10.6557	−0.672584	−0.336292	−	0.941758i	$-0.609173\pi$
$251$	−10.6557	−0.672584	−0.336292	+	0.941758i	$0.609173\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	−10.6978	−0.669921
$256$	0	0
$257$	2.80906	0.175224	0.0876121	−	0.996155i	$-0.472076\pi$
$257$	2.80906	0.175224	0.0876121	+	0.996155i	$0.472076\pi$
$258$	0	0
$259$	−9.12797	−0.567185
$260$	0	0
$261$	24.4994	1.51647
$262$	0	0
$263$	−27.6453	−1.70468	−0.852340	−	0.522987i	$-0.824817\pi$
$263$	−27.6453	−1.70468	−0.852340	+	0.522987i	$0.824817\pi$
$264$	0	0
$265$	2.51730	0.154637
$266$	0	0
$267$	−30.9596	−1.89469
$268$	0	0
$269$	−14.5761	−0.888718	−0.444359	−	0.895849i	$-0.646569\pi$
$269$	−14.5761	−0.888718	−0.444359	+	0.895849i	$0.646569\pi$
$270$	0	0
$271$	2.16258	0.131367	0.0656837	−	0.997840i	$-0.479077\pi$
$271$	2.16258	0.131367	0.0656837	+	0.997840i	$0.479077\pi$
$272$	0	0
$273$	−14.3789	−0.870249
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−15.3022	−0.919421	−0.459710	−	0.888069i	$-0.652047\pi$
$277$	−15.3022	−0.919421	−0.459710	+	0.888069i	$0.652047\pi$
$278$	0	0
$279$	−48.0576	−2.87713
$280$	0	0
$281$	2.13843	0.127568	0.0637841	−	0.997964i	$-0.479683\pi$
$281$	2.13843	0.127568	0.0637841	+	0.997964i	$0.479683\pi$
$282$	0	0
$283$	−4.33099	−0.257451	−0.128725	−	0.991680i	$-0.541089\pi$
$283$	−4.33099	−0.257451	−0.128725	+	0.991680i	$0.541089\pi$
$284$	0	0
$285$	9.21509	0.545855
$286$	0	0
$287$	15.4014	0.909116
$288$	0	0
$289$	−3.06922	−0.180542
$290$	0	0
$291$	−31.5761	−1.85102
$292$	0	0
$293$	−13.5068	−0.789078	−0.394539	−	0.918879i	$-0.629096\pi$
$293$	−13.5068	−0.789078	−0.394539	+	0.918879i	$0.629096\pi$
$294$	0	0
$295$	11.9129	0.693595
$296$	0	0
$297$	0	0
$298$	0	0
$299$	3.73240	0.215850
$300$	0	0
$301$	−18.2151	−1.04990
$302$	0	0
$303$	36.4936	2.09650
$304$	0	0
$305$	13.6799	0.783308
$306$	0	0
$307$	2.37887	0.135769	0.0678847	−	0.997693i	$-0.478375\pi$
$307$	2.37887	0.135769	0.0678847	+	0.997693i	$0.478375\pi$
$308$	0	0
$309$	−52.5749	−2.99088
$310$	0	0
$311$	22.1447	1.25571	0.627855	−	0.778331i	$-0.283933\pi$
$311$	22.1447	1.25571	0.627855	+	0.778331i	$0.283933\pi$
$312$	0	0
$313$	−27.2843	−1.54220	−0.771100	−	0.636714i	$-0.780293\pi$
$313$	−27.2843	−1.54220	−0.771100	+	0.636714i	$0.780293\pi$
$314$	0	0
$315$	−17.6453	−0.994199
$316$	0	0
$317$	−15.3956	−0.864702	−0.432351	−	0.901705i	$-0.642316\pi$
$317$	−15.3956	−0.864702	−0.432351	+	0.901705i	$0.642316\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	20.4469	1.14123
$322$	0	0
$323$	−12.0000	−0.667698
$324$	0	0
$325$	1.48270	0.0822452
$326$	0	0
$327$	−11.8829	−0.657126
$328$	0	0
$329$	35.6262	1.96413
$330$	0	0
$331$	−25.9129	−1.42430	−0.712150	−	0.702027i	$-0.752279\pi$
$331$	−25.9129	−1.42430	−0.712150	+	0.702027i	$0.752279\pi$
$332$	0	0
$333$	−14.0692	−0.770988
$334$	0	0
$335$	7.83159	0.427885
$336$	0	0
$337$	13.9821	0.761653	0.380827	−	0.924646i	$-0.375639\pi$
$337$	13.9821	0.761653	0.380827	+	0.924646i	$0.375639\pi$
$338$	0	0
$339$	−4.19839	−0.228025
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−8.63440	−0.466214
$344$	0	0
$345$	7.21509	0.388448
$346$	0	0
$347$	31.0467	1.66667	0.833337	−	0.552766i	$-0.186428\pi$
$347$	31.0467	1.66667	0.833337	+	0.552766i	$0.186428\pi$
$348$	0	0
$349$	3.66318	0.196086	0.0980428	−	0.995182i	$-0.468742\pi$
$349$	3.66318	0.196086	0.0980428	+	0.995182i	$0.468742\pi$
$350$	0	0
$351$	−9.41348	−0.502454
$352$	0	0
$353$	24.5749	1.30799	0.653994	−	0.756500i	$-0.273092\pi$
$353$	24.5749	1.30799	0.653994	+	0.756500i	$0.273092\pi$
$354$	0	0
$355$	2.51730	0.133605
$356$	0	0
$357$	36.1960	1.91570
$358$	0	0
$359$	6.58652	0.347623	0.173812	−	0.984779i	$-0.444392\pi$
$359$	6.58652	0.347623	0.173812	+	0.984779i	$0.444392\pi$
$360$	0	0
$361$	−8.66318	−0.455957
$362$	0	0
$363$	0	0
$364$	0	0
$365$	2.96539	0.155216
$366$	0	0
$367$	−8.16841	−0.426388	−0.213194	−	0.977010i	$-0.568387\pi$
$367$	−8.16841	−0.426388	−0.213194	+	0.977010i	$0.568387\pi$
$368$	0	0
$369$	23.7386	1.23578
$370$	0	0
$371$	−8.51730	−0.442196
$372$	0	0
$373$	−27.0409	−1.40012	−0.700061	−	0.714083i	$-0.746844\pi$
$373$	−27.0409	−1.40012	−0.700061	+	0.714083i	$0.746844\pi$
$374$	0	0
$375$	2.86620	0.148010
$376$	0	0
$377$	6.96539	0.358736
$378$	0	0
$379$	−32.6620	−1.67773	−0.838867	−	0.544337i	$-0.816781\pi$
$379$	−32.6620	−1.67773	−0.838867	+	0.544337i	$0.816781\pi$
$380$	0	0
$381$	32.3777	1.65876
$382$	0	0
$383$	2.64648	0.135229	0.0676143	−	0.997712i	$-0.478461\pi$
$383$	2.64648	0.135229	0.0676143	+	0.997712i	$0.478461\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−28.0755	−1.42716
$388$	0	0
$389$	−29.0513	−1.47296	−0.736480	−	0.676459i	$-0.763513\pi$
$389$	−29.0513	−1.47296	−0.736480	+	0.676459i	$0.763513\pi$
$390$	0	0
$391$	−9.39558	−0.475155
$392$	0	0
$393$	−42.0755	−2.12243
$394$	0	0
$395$	6.76700	0.340485
$396$	0	0
$397$	−9.35977	−0.469753	−0.234877	−	0.972025i	$-0.575469\pi$
$397$	−9.35977	−0.469753	−0.234877	+	0.972025i	$0.575469\pi$
$398$	0	0
$399$	−31.1793	−1.56092
$400$	0	0
$401$	4.93078	0.246232	0.123116	−	0.992392i	$-0.460711\pi$
$401$	4.93078	0.246232	0.123116	+	0.992392i	$0.460711\pi$
$402$	0	0
$403$	−13.6632	−0.680611
$404$	0	0
$405$	−2.55191	−0.126806
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−38.3085	−1.89423	−0.947116	−	0.320892i	$-0.896017\pi$
$409$	−38.3085	−1.89423	−0.947116	+	0.320892i	$0.896017\pi$
$410$	0	0
$411$	44.8425	2.21192
$412$	0	0
$413$	−40.3073	−1.98339
$414$	0	0
$415$	7.55191	0.370709
$416$	0	0
$417$	21.9129	1.07308
$418$	0	0
$419$	−37.3777	−1.82602	−0.913009	−	0.407938i	$-0.866248\pi$
$419$	−37.3777	−1.82602	−0.913009	+	0.407938i	$0.866248\pi$
$420$	0	0
$421$	29.4123	1.43347	0.716733	−	0.697347i	$-0.245636\pi$
$421$	29.4123	1.43347	0.716733	+	0.697347i	$0.245636\pi$
$422$	0	0
$423$	54.9117	2.66990
$424$	0	0
$425$	−3.73240	−0.181048
$426$	0	0
$427$	−46.2859	−2.23993
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−1.76820	−0.0851713	−0.0425857	−	0.999093i	$-0.513560\pi$
$431$	−1.76820	−0.0851713	−0.0425857	+	0.999093i	$0.513560\pi$
$432$	0	0
$433$	10.0513	0.483035	0.241518	−	0.970396i	$-0.422355\pi$
$433$	10.0513	0.483035	0.241518	+	0.970396i	$0.422355\pi$
$434$	0	0
$435$	13.4648	0.645587
$436$	0	0
$437$	8.09337	0.387158
$438$	0	0
$439$	−39.1972	−1.87078	−0.935390	−	0.353618i	$-0.884951\pi$
$439$	−39.1972	−1.87078	−0.935390	+	0.353618i	$0.884951\pi$
$440$	0	0
$441$	23.1972	1.10463
$442$	0	0
$443$	14.0121	0.665734	0.332867	−	0.942974i	$-0.391984\pi$
$443$	14.0121	0.665734	0.332867	+	0.942974i	$0.391984\pi$
$444$	0	0
$445$	−10.8016	−0.512046
$446$	0	0
$447$	−18.5807	−0.878837
$448$	0	0
$449$	2.57606	0.121572	0.0607859	−	0.998151i	$-0.480639\pi$
$449$	2.57606	0.121572	0.0607859	+	0.998151i	$0.480639\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	31.1793	1.46493
$454$	0	0
$455$	−5.01671	−0.235187
$456$	0	0
$457$	15.1217	0.707365	0.353682	−	0.935366i	$-0.384929\pi$
$457$	15.1217	0.707365	0.353682	+	0.935366i	$0.384929\pi$
$458$	0	0
$459$	23.6966	1.10606
$460$	0	0
$461$	9.83622	0.458118	0.229059	−	0.973412i	$-0.426435\pi$
$461$	9.83622	0.458118	0.229059	+	0.973412i	$0.426435\pi$
$462$	0	0
$463$	−21.2093	−0.985678	−0.492839	−	0.870120i	$-0.664041\pi$
$463$	−21.2093	−0.985678	−0.492839	+	0.870120i	$0.664041\pi$
$464$	0	0
$465$	−26.4123	−1.22484
$466$	0	0
$467$	9.56399	0.442569	0.221284	−	0.975209i	$-0.428975\pi$
$467$	9.56399	0.442569	0.221284	+	0.975209i	$0.428975\pi$
$468$	0	0
$469$	−26.4982	−1.22357
$470$	0	0
$471$	−29.8950	−1.37749
$472$	0	0
$473$	0	0
$474$	0	0
$475$	3.21509	0.147519
$476$	0	0
$477$	−13.1280	−0.601089
$478$	0	0
$479$	17.1972	0.785760	0.392880	−	0.919590i	$-0.371479\pi$
$479$	17.1972	0.785760	0.392880	+	0.919590i	$0.371479\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	0	0
$483$	−24.4123	−1.11080
$484$	0	0
$485$	−11.0167	−0.500243
$486$	0	0
$487$	−15.5519	−0.704724	−0.352362	−	0.935864i	$-0.614621\pi$
$487$	−15.5519	−0.704724	−0.352362	+	0.935864i	$0.614621\pi$
$488$	0	0
$489$	−29.3610	−1.32775
$490$	0	0
$491$	9.05876	0.408816	0.204408	−	0.978886i	$-0.434473\pi$
$491$	9.05876	0.408816	0.204408	+	0.978886i	$0.434473\pi$
$492$	0	0
$493$	−17.5340	−0.789692
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−8.51730	−0.382053
$498$	0	0
$499$	−24.5686	−1.09984	−0.549921	−	0.835217i	$-0.685342\pi$
$499$	−24.5686	−1.09984	−0.549921	+	0.835217i	$0.685342\pi$
$500$	0	0
$501$	−3.00000	−0.134030
$502$	0	0
$503$	11.3322	0.505277	0.252639	−	0.967561i	$-0.418702\pi$
$503$	11.3322	0.505277	0.252639	+	0.967561i	$0.418702\pi$
$504$	0	0
$505$	12.7324	0.566584
$506$	0	0
$507$	30.9596	1.37496
$508$	0	0
$509$	−26.4889	−1.17410	−0.587051	−	0.809550i	$-0.699711\pi$
$509$	−26.4889	−1.17410	−0.587051	+	0.809550i	$0.699711\pi$
$510$	0	0
$511$	−10.0334	−0.443852
$512$	0	0
$513$	−20.4123	−0.901224
$514$	0	0
$515$	−18.3431	−0.808292
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−34.1447	−1.49879
$520$	0	0
$521$	26.6966	1.16960	0.584799	−	0.811178i	$-0.301173\pi$
$521$	26.6966	1.16960	0.584799	+	0.811178i	$0.301173\pi$
$522$	0	0
$523$	4.85412	0.212256	0.106128	−	0.994352i	$-0.466155\pi$
$523$	4.85412	0.212256	0.106128	+	0.994352i	$0.466155\pi$
$524$	0	0
$525$	−9.69779	−0.423246
$526$	0	0
$527$	34.3944	1.49824
$528$	0	0
$529$	−16.6632	−0.724486
$530$	0	0
$531$	−62.1268	−2.69607
$532$	0	0
$533$	6.74910	0.292336
$534$	0	0
$535$	7.13380	0.308421
$536$	0	0
$537$	−9.73240	−0.419984
$538$	0	0
$539$	0	0
$540$	0	0
$541$	19.8246	0.852325	0.426162	−	0.904647i	$-0.359865\pi$
$541$	19.8246	0.852325	0.426162	+	0.904647i	$0.359865\pi$
$542$	0	0
$543$	16.3310	0.700830
$544$	0	0
$545$	−4.14588	−0.177590
$546$	0	0
$547$	−14.6557	−0.626634	−0.313317	−	0.949649i	$-0.601440\pi$
$547$	−14.6557	−0.626634	−0.313317	+	0.949649i	$0.601440\pi$
$548$	0	0
$549$	−71.3419	−3.04480
$550$	0	0
$551$	15.1038	0.643445
$552$	0	0
$553$	−22.8962	−0.973644
$554$	0	0
$555$	−7.73240	−0.328222
$556$	0	0
$557$	5.83742	0.247339	0.123670	−	0.992323i	$-0.460534\pi$
$557$	5.83742	0.247339	0.123670	+	0.992323i	$0.460534\pi$
$558$	0	0
$559$	−7.98210	−0.337607
$560$	0	0
$561$	0	0
$562$	0	0
$563$	39.3026	1.65641	0.828204	−	0.560426i	$-0.189363\pi$
$563$	39.3026	1.65641	0.828204	+	0.560426i	$0.189363\pi$
$564$	0	0
$565$	−1.46479	−0.0616243
$566$	0	0
$567$	8.63440	0.362611
$568$	0	0
$569$	−8.11007	−0.339992	−0.169996	−	0.985445i	$-0.554375\pi$
$569$	−8.11007	−0.339992	−0.169996	+	0.985445i	$0.554375\pi$
$570$	0	0
$571$	−35.6274	−1.49096	−0.745480	−	0.666528i	$-0.767780\pi$
$571$	−35.6274	−1.49096	−0.745480	+	0.666528i	$0.767780\pi$
$572$	0	0
$573$	−25.8437	−1.07963
$574$	0	0
$575$	2.51730	0.104979
$576$	0	0
$577$	−31.8529	−1.32605	−0.663027	−	0.748595i	$-0.730729\pi$
$577$	−31.8529	−1.32605	−0.663027	+	0.748595i	$0.730729\pi$
$578$	0	0
$579$	−75.1855	−3.12460
$580$	0	0
$581$	−25.5519	−1.06007
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−7.73240	−0.319695
$586$	0	0
$587$	44.3823	1.83185	0.915927	−	0.401345i	$-0.131457\pi$
$587$	44.3823	1.83185	0.915927	+	0.401345i	$0.131457\pi$
$588$	0	0
$589$	−29.6274	−1.22077
$590$	0	0
$591$	47.8592	1.96866
$592$	0	0
$593$	−41.9463	−1.72253	−0.861264	−	0.508158i	$-0.830327\pi$
$593$	−41.9463	−1.72253	−0.861264	+	0.508158i	$0.830327\pi$
$594$	0	0
$595$	12.6286	0.517721
$596$	0	0
$597$	−48.1268	−1.96970
$598$	0	0
$599$	−16.6107	−0.678694	−0.339347	−	0.940661i	$-0.610206\pi$
$599$	−16.6107	−0.678694	−0.339347	+	0.940661i	$0.610206\pi$
$600$	0	0
$601$	−13.1972	−0.538325	−0.269162	−	0.963095i	$-0.586747\pi$
$601$	−13.1972	−0.538325	−0.269162	+	0.963095i	$0.586747\pi$
$602$	0	0
$603$	−40.8425	−1.66323
$604$	0	0
$605$	0	0
$606$	0	0
$607$	9.04085	0.366957	0.183478	−	0.983024i	$-0.441264\pi$
$607$	9.04085	0.366957	0.183478	+	0.983024i	$0.441264\pi$
$608$	0	0
$609$	−45.5582	−1.84611
$610$	0	0
$611$	15.6119	0.631589
$612$	0	0
$613$	−7.66318	−0.309513	−0.154756	−	0.987953i	$-0.549459\pi$
$613$	−7.66318	−0.309513	−0.154756	+	0.987953i	$0.549459\pi$
$614$	0	0
$615$	13.0467	0.526093
$616$	0	0
$617$	−2.67989	−0.107888	−0.0539441	−	0.998544i	$-0.517179\pi$
$617$	−2.67989	−0.107888	−0.0539441	+	0.998544i	$0.517179\pi$
$618$	0	0
$619$	−8.17424	−0.328550	−0.164275	−	0.986415i	$-0.552529\pi$
$619$	−8.17424	−0.328550	−0.164275	+	0.986415i	$0.552529\pi$
$620$	0	0
$621$	−15.9821	−0.641339
$622$	0	0
$623$	36.5473	1.46424
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	10.0692	0.401486
$630$	0	0
$631$	−5.56982	−0.221731	−0.110865	−	0.993835i	$-0.535362\pi$
$631$	−5.56982	−0.221731	−0.110865	+	0.993835i	$0.535362\pi$
$632$	0	0
$633$	21.9129	0.870959
$634$	0	0
$635$	11.2964	0.448283
$636$	0	0
$637$	6.59516	0.261310
$638$	0	0
$639$	−13.1280	−0.519335
$640$	0	0
$641$	−13.2906	−0.524945	−0.262473	−	0.964939i	$-0.584538\pi$
$641$	−13.2906	−0.524945	−0.262473	+	0.964939i	$0.584538\pi$
$642$	0	0
$643$	−17.8137	−0.702503	−0.351252	−	0.936281i	$-0.614244\pi$
$643$	−17.8137	−0.702503	−0.351252	+	0.936281i	$0.614244\pi$
$644$	0	0
$645$	−15.4302	−0.607563
$646$	0	0
$647$	25.8829	1.01756	0.508781	−	0.860896i	$-0.330096\pi$
$647$	25.8829	1.01756	0.508781	+	0.860896i	$0.330096\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	89.3660	3.50253
$652$	0	0
$653$	13.3356	0.521863	0.260932	−	0.965357i	$-0.415970\pi$
$653$	13.3356	0.521863	0.260932	+	0.965357i	$0.415970\pi$
$654$	0	0
$655$	−14.6799	−0.573591
$656$	0	0
$657$	−15.4648	−0.603339
$658$	0	0
$659$	24.4877	0.953907	0.476954	−	0.878929i	$-0.341741\pi$
$659$	24.4877	0.953907	0.476954	+	0.878929i	$0.341741\pi$
$660$	0	0
$661$	−23.2738	−0.905248	−0.452624	−	0.891702i	$-0.649512\pi$
$661$	−23.2738	−0.905248	−0.452624	+	0.891702i	$0.649512\pi$
$662$	0	0
$663$	15.8616	0.616012
$664$	0	0
$665$	−10.8783	−0.421841
$666$	0	0
$667$	11.8258	0.457895
$668$	0	0
$669$	−10.8616	−0.419932
$670$	0	0
$671$	0	0
$672$	0	0
$673$	11.3443	0.437289	0.218645	−	0.975805i	$-0.429836\pi$
$673$	11.3443	0.437289	0.218645	+	0.975805i	$0.429836\pi$
$674$	0	0
$675$	−6.34889	−0.244369
$676$	0	0
$677$	−21.3956	−0.822299	−0.411149	−	0.911568i	$-0.634873\pi$
$677$	−21.3956	−0.822299	−0.411149	+	0.911568i	$0.634873\pi$
$678$	0	0
$679$	37.2750	1.43049
$680$	0	0
$681$	−56.0230	−2.14680
$682$	0	0
$683$	5.11590	0.195754	0.0978772	−	0.995198i	$-0.468795\pi$
$683$	5.11590	0.195754	0.0978772	+	0.995198i	$0.468795\pi$
$684$	0	0
$685$	15.6453	0.597775
$686$	0	0
$687$	−14.7970	−0.564540
$688$	0	0
$689$	−3.73240	−0.142193
$690$	0	0
$691$	22.9117	0.871602	0.435801	−	0.900043i	$-0.356465\pi$
$691$	22.9117	0.871602	0.435801	+	0.900043i	$0.356465\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	7.64528	0.290002
$696$	0	0
$697$	−16.9895	−0.643525
$698$	0	0
$699$	−17.9129	−0.677527
$700$	0	0
$701$	−37.9191	−1.43219	−0.716093	−	0.698005i	$-0.754071\pi$
$701$	−37.9191	−1.43219	−0.716093	+	0.698005i	$0.754071\pi$
$702$	0	0
$703$	−8.67364	−0.327133
$704$	0	0
$705$	30.1793	1.13662
$706$	0	0
$707$	−43.0801	−1.62019
$708$	0	0
$709$	−5.27686	−0.198177	−0.0990884	−	0.995079i	$-0.531593\pi$
$709$	−5.27686	−0.198177	−0.0990884	+	0.995079i	$0.531593\pi$
$710$	0	0
$711$	−35.2906	−1.32350
$712$	0	0
$713$	−23.1972	−0.868742
$714$	0	0
$715$	0	0
$716$	0	0
$717$	13.2151	0.493527
$718$	0	0
$719$	−30.9117	−1.15281	−0.576406	−	0.817164i	$-0.695545\pi$
$719$	−30.9117	−1.15281	−0.576406	+	0.817164i	$0.695545\pi$
$720$	0	0
$721$	62.0638	2.31138
$722$	0	0
$723$	−22.5807	−0.839785
$724$	0	0
$725$	4.69779	0.174471
$726$	0	0
$727$	−8.24387	−0.305748	−0.152874	−	0.988246i	$-0.548853\pi$
$727$	−8.24387	−0.305748	−0.152874	+	0.988246i	$0.548853\pi$
$728$	0	0
$729$	−41.2831	−1.52900
$730$	0	0
$731$	20.0934	0.743180
$732$	0	0
$733$	43.3839	1.60242	0.801211	−	0.598382i	$-0.204190\pi$
$733$	43.3839	1.60242	0.801211	+	0.598382i	$0.204190\pi$
$734$	0	0
$735$	12.7491	0.470258
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−0.301014	−0.0110730	−0.00553649	−	0.999985i	$-0.501762\pi$
$739$	−0.301014	−0.0110730	−0.00553649	+	0.999985i	$0.501762\pi$
$740$	0	0
$741$	−13.6632	−0.501929
$742$	0	0
$743$	−31.5040	−1.15577	−0.577885	−	0.816118i	$-0.696122\pi$
$743$	−31.5040	−1.15577	−0.577885	+	0.816118i	$0.696122\pi$
$744$	0	0
$745$	−6.48270	−0.237508
$746$	0	0
$747$	−39.3839	−1.44098
$748$	0	0
$749$	−24.1372	−0.881955
$750$	0	0
$751$	−33.2906	−1.21479	−0.607395	−	0.794400i	$-0.707785\pi$
$751$	−33.2906	−1.21479	−0.607395	+	0.794400i	$0.707785\pi$
$752$	0	0
$753$	30.5415	1.11299
$754$	0	0
$755$	10.8783	0.395901
$756$	0	0
$757$	15.5068	0.563606	0.281803	−	0.959472i	$-0.409068\pi$
$757$	15.5068	0.563606	0.281803	+	0.959472i	$0.409068\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−52.3944	−1.89929	−0.949647	−	0.313321i	$-0.898559\pi$
$761$	−52.3944	−1.89929	−0.949647	+	0.313321i	$0.898559\pi$
$762$	0	0
$763$	14.0276	0.507833
$764$	0	0
$765$	19.4648	0.703751
$766$	0	0
$767$	−17.6632	−0.637780
$768$	0	0
$769$	44.2652	1.59624	0.798122	−	0.602496i	$-0.205827\pi$
$769$	44.2652	1.59624	0.798122	+	0.602496i	$0.205827\pi$
$770$	0	0
$771$	−8.05131	−0.289961
$772$	0	0
$773$	−35.3177	−1.27029	−0.635145	−	0.772393i	$-0.719060\pi$
$773$	−35.3177	−1.27029	−0.635145	+	0.772393i	$0.719060\pi$
$774$	0	0
$775$	−9.21509	−0.331016
$776$	0	0
$777$	26.1626	0.938577
$778$	0	0
$779$	14.6348	0.524347
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−29.8258	−1.06589
$784$	0	0
$785$	−10.4302	−0.372269
$786$	0	0
$787$	36.6920	1.30793	0.653964	−	0.756526i	$-0.273105\pi$
$787$	36.6920	1.30793	0.653964	+	0.756526i	$0.273105\pi$
$788$	0	0
$789$	79.2368	2.82091
$790$	0	0
$791$	4.95613	0.176220
$792$	0	0
$793$	−20.2831	−0.720274
$794$	0	0
$795$	−7.21509	−0.255893
$796$	0	0
$797$	−2.85412	−0.101098	−0.0505491	−	0.998722i	$-0.516097\pi$
$797$	−2.85412	−0.101098	−0.0505491	+	0.998722i	$0.516097\pi$
$798$	0	0
$799$	−39.2998	−1.39033
$800$	0	0
$801$	56.3314	1.99037
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−8.51730	−0.300196
$806$	0	0
$807$	41.7779	1.47065
$808$	0	0
$809$	−26.0934	−0.917394	−0.458697	−	0.888593i	$-0.651684\pi$
$809$	−26.0934	−0.917394	−0.458697	+	0.888593i	$0.651684\pi$
$810$	0	0
$811$	−19.6453	−0.689839	−0.344919	−	0.938632i	$-0.612094\pi$
$811$	−19.6453	−0.689839	−0.344919	+	0.938632i	$0.612094\pi$
$812$	0	0
$813$	−6.19839	−0.217387
$814$	0	0
$815$	−10.2439	−0.358827
$816$	0	0
$817$	−17.3085	−0.605546
$818$	0	0
$819$	26.1626	0.914195
$820$	0	0
$821$	51.9117	1.81173	0.905865	−	0.423566i	$-0.139222\pi$
$821$	51.9117	1.81173	0.905865	+	0.423566i	$0.139222\pi$
$822$	0	0
$823$	−15.9250	−0.555109	−0.277555	−	0.960710i	$-0.589524\pi$
$823$	−15.9250	−0.555109	−0.277555	+	0.960710i	$0.589524\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	9.77164	0.339793	0.169897	−	0.985462i	$-0.445657\pi$
$827$	9.77164	0.339793	0.169897	+	0.985462i	$0.445657\pi$
$828$	0	0
$829$	1.01790	0.0353532	0.0176766	−	0.999844i	$-0.494373\pi$
$829$	1.01790	0.0353532	0.0176766	+	0.999844i	$0.494373\pi$
$830$	0	0
$831$	43.8592	1.52146
$832$	0	0
$833$	−16.6020	−0.575226
$834$	0	0
$835$	−1.04668	−0.0362219
$836$	0	0
$837$	58.5056	2.02225
$838$	0	0
$839$	−13.7900	−0.476082	−0.238041	−	0.971255i	$-0.576505\pi$
$839$	−13.7900	−0.476082	−0.238041	+	0.971255i	$0.576505\pi$
$840$	0	0
$841$	−6.93078	−0.238993
$842$	0	0
$843$	−6.12917	−0.211100
$844$	0	0
$845$	10.8016	0.371587
$846$	0	0
$847$	0	0
$848$	0	0
$849$	12.4135	0.426030
$850$	0	0
$851$	−6.79115	−0.232798
$852$	0	0
$853$	27.3264	0.935637	0.467818	−	0.883825i	$-0.345040\pi$
$853$	27.3264	0.935637	0.467818	+	0.883825i	$0.345040\pi$
$854$	0	0
$855$	−16.7670	−0.573419
$856$	0	0
$857$	22.2318	0.759424	0.379712	−	0.925105i	$-0.376023\pi$
$857$	22.2318	0.759424	0.379712	+	0.925105i	$0.376023\pi$
$858$	0	0
$859$	−28.5173	−0.972998	−0.486499	−	0.873681i	$-0.661726\pi$
$859$	−28.5173	−0.972998	−0.486499	+	0.873681i	$0.661726\pi$
$860$	0	0
$861$	−44.1435	−1.50441
$862$	0	0
$863$	−52.2594	−1.77893	−0.889465	−	0.457003i	$-0.848923\pi$
$863$	−52.2594	−1.77893	−0.889465	+	0.457003i	$0.848923\pi$
$864$	0	0
$865$	−11.9129	−0.405050
$866$	0	0
$867$	8.79698	0.298761
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−11.6119	−0.393453
$872$	0	0
$873$	57.4531	1.94449
$874$	0	0
$875$	−3.38350	−0.114383
$876$	0	0
$877$	−21.0074	−0.709371	−0.354685	−	0.934986i	$-0.615412\pi$
$877$	−21.0074	−0.709371	−0.354685	+	0.934986i	$0.615412\pi$
$878$	0	0
$879$	38.7133	1.30577
$880$	0	0
$881$	46.0743	1.55228	0.776141	−	0.630560i	$-0.217175\pi$
$881$	46.0743	1.55228	0.776141	+	0.630560i	$0.217175\pi$
$882$	0	0
$883$	−0.622326	−0.0209429	−0.0104715	−	0.999945i	$-0.503333\pi$
$883$	−0.622326	−0.0209429	−0.0104715	+	0.999945i	$0.503333\pi$
$884$	0	0
$885$	−34.1447	−1.14776
$886$	0	0
$887$	−11.4077	−0.383031	−0.191516	−	0.981490i	$-0.561340\pi$
$887$	−11.4077	−0.383031	−0.191516	+	0.981490i	$0.561340\pi$
$888$	0	0
$889$	−38.2213	−1.28190
$890$	0	0
$891$	0	0
$892$	0	0
$893$	33.8529	1.13284
$894$	0	0
$895$	−3.39558	−0.113502
$896$	0	0
$897$	−10.6978	−0.357189
$898$	0	0
$899$	−43.2906	−1.44382
$900$	0	0
$901$	9.39558	0.313012
$902$	0	0
$903$	52.2081	1.73738
$904$	0	0
$905$	5.69779	0.189401
$906$	0	0
$907$	−38.9175	−1.29223	−0.646117	−	0.763238i	$-0.723608\pi$
$907$	−38.9175	−1.29223	−0.646117	+	0.763238i	$0.723608\pi$
$908$	0	0
$909$	−66.4006	−2.20237
$910$	0	0
$911$	−38.0934	−1.26209	−0.631045	−	0.775746i	$-0.717374\pi$
$911$	−38.0934	−1.26209	−0.631045	+	0.775746i	$0.717374\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−39.2093	−1.29622
$916$	0	0
$917$	49.6694	1.64023
$918$	0	0
$919$	19.2727	0.635746	0.317873	−	0.948133i	$-0.397031\pi$
$919$	19.2727	0.635746	0.317873	+	0.948133i	$0.397031\pi$
$920$	0	0
$921$	−6.81832	−0.224671
$922$	0	0
$923$	−3.73240	−0.122853
$924$	0	0
$925$	−2.69779	−0.0887027
$926$	0	0
$927$	95.6608	3.14191
$928$	0	0
$929$	31.1730	1.02275	0.511377	−	0.859356i	$-0.329136\pi$
$929$	31.1730	1.02275	0.511377	+	0.859356i	$0.329136\pi$
$930$	0	0
$931$	14.3010	0.468697
$932$	0	0
$933$	−63.4710	−2.07795
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−25.8708	−0.845163	−0.422582	−	0.906325i	$-0.638876\pi$
$937$	−25.8708	−0.845163	−0.422582	+	0.906325i	$0.638876\pi$
$938$	0	0
$939$	78.2022	2.55203
$940$	0	0
$941$	−29.4636	−0.960486	−0.480243	−	0.877136i	$-0.659451\pi$
$941$	−29.4636	−0.960486	−0.480243	+	0.877136i	$0.659451\pi$
$942$	0	0
$943$	11.4585	0.373142
$944$	0	0
$945$	21.4815	0.698793
$946$	0	0
$947$	14.3881	0.467551	0.233776	−	0.972291i	$-0.424892\pi$
$947$	14.3881	0.467551	0.233776	+	0.972291i	$0.424892\pi$
$948$	0	0
$949$	−4.39677	−0.142725
$950$	0	0
$951$	44.1268	1.43091
$952$	0	0
$953$	31.9191	1.03396	0.516981	−	0.855997i	$-0.327056\pi$
$953$	31.9191	1.03396	0.516981	+	0.855997i	$0.327056\pi$
$954$	0	0
$955$	−9.01671	−0.291774
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−52.9358	−1.70939
$960$	0	0
$961$	53.9179	1.73929
$962$	0	0
$963$	−37.2034	−1.19886
$964$	0	0
$965$	−26.2318	−0.844431
$966$	0	0
$967$	46.8425	1.50635	0.753176	−	0.657819i	$-0.228521\pi$
$967$	46.8425	1.50635	0.753176	+	0.657819i	$0.228521\pi$
$968$	0	0
$969$	34.3944	1.10491
$970$	0	0
$971$	6.66198	0.213793	0.106897	−	0.994270i	$-0.465909\pi$
$971$	6.66198	0.213793	0.106897	+	0.994270i	$0.465909\pi$
$972$	0	0
$973$	−25.8678	−0.829284
$974$	0	0
$975$	−4.24970	−0.136099
$976$	0	0
$977$	−24.1960	−0.774098	−0.387049	−	0.922059i	$-0.626506\pi$
$977$	−24.1960	−0.774098	−0.387049	+	0.922059i	$0.626506\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	21.6211	0.690310
$982$	0	0
$983$	27.7716	0.885778	0.442889	−	0.896577i	$-0.353954\pi$
$983$	27.7716	0.885778	0.442889	+	0.896577i	$0.353954\pi$
$984$	0	0
$985$	16.6978	0.532036
$986$	0	0
$987$	−102.112	−3.25025
$988$	0	0
$989$	−13.5519	−0.430926
$990$	0	0
$991$	−45.4227	−1.44290	−0.721450	−	0.692466i	$-0.756524\pi$
$991$	−45.4227	−1.44290	−0.721450	+	0.692466i	$0.756524\pi$
$992$	0	0
$993$	74.2715	2.35693
$994$	0	0
$995$	−16.7912	−0.532315
$996$	0	0
$997$	−50.7491	−1.60724	−0.803620	−	0.595143i	$-0.797096\pi$
$997$	−50.7491	−1.60724	−0.803620	+	0.595143i	$0.797096\pi$
$998$	0	0
$999$	17.1280	0.541905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9680.2.a.cb.1.1		3
4.3	odd	2		605.2.a.h.1.3	yes	3
11.10	odd	2		9680.2.a.bz.1.1		3
12.11	even	2		5445.2.a.bb.1.1		3
20.19	odd	2		3025.2.a.p.1.1		3
44.3	odd	10		605.2.g.o.251.3		12
44.7	even	10		605.2.g.p.511.1		12
44.15	odd	10		605.2.g.o.511.3		12
44.19	even	10		605.2.g.p.251.1		12
44.27	odd	10		605.2.g.o.366.1		12
44.31	odd	10		605.2.g.o.81.1		12
44.35	even	10		605.2.g.p.81.3		12
44.39	even	10		605.2.g.p.366.3		12
44.43	even	2		605.2.a.g.1.1	✓	3
132.131	odd	2		5445.2.a.bd.1.3		3
220.219	even	2		3025.2.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.1	✓	3	44.43	even	2
605.2.a.h.1.3	yes	3	4.3	odd	2
605.2.g.o.81.1		12	44.31	odd	10
605.2.g.o.251.3		12	44.3	odd	10
605.2.g.o.366.1		12	44.27	odd	10
605.2.g.o.511.3		12	44.15	odd	10
605.2.g.p.81.3		12	44.35	even	10
605.2.g.p.251.1		12	44.19	even	10
605.2.g.p.366.3		12	44.39	even	10
605.2.g.p.511.1		12	44.7	even	10
3025.2.a.p.1.1		3	20.19	odd	2
3025.2.a.u.1.3		3	220.219	even	2
5445.2.a.bb.1.1		3	12.11	even	2
5445.2.a.bd.1.3		3	132.131	odd	2
9680.2.a.bz.1.1		3	11.10	odd	2
9680.2.a.cb.1.1		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9680.a (trivial)

\(f(q)\)	\(=\)	\(q-2.86620 q^{3} -1.00000 q^{5} +3.38350 q^{7} +5.21509 q^{9} +O(q^{10})\)	\(q-2.86620 q^{3} -1.00000 q^{5} +3.38350 q^{7} +5.21509 q^{9} +1.48270 q^{13} +2.86620 q^{15} -3.73240 q^{17} +3.21509 q^{19} -9.69779 q^{21} +2.51730 q^{23} +1.00000 q^{25} -6.34889 q^{27} +4.69779 q^{29} -9.21509 q^{31} -3.38350 q^{35} -2.69779 q^{37} -4.24970 q^{39} +4.55191 q^{41} -5.38350 q^{43} -5.21509 q^{45} +10.5294 q^{47} +4.44809 q^{49} +10.6978 q^{51} -2.51730 q^{53} -9.21509 q^{57} -11.9129 q^{59} -13.6799 q^{61} +17.6453 q^{63} -1.48270 q^{65} -7.83159 q^{67} -7.21509 q^{69} -2.51730 q^{71} -2.96539 q^{73} -2.86620 q^{75} -6.76700 q^{79} +2.55191 q^{81} -7.55191 q^{83} +3.73240 q^{85} -13.4648 q^{87} +10.8016 q^{89} +5.01671 q^{91} +26.4123 q^{93} -3.21509 q^{95} +11.0167 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{3} - 3 q^{5} + q^{7} + 2 q^{9}+O(q^{10}) \) 3 * q - q^3 - 3 * q^5 + q^7 + 2 * q^9	\( 3 q - q^{3} - 3 q^{5} + q^{7} + 2 q^{9} + 6 q^{13} + q^{15} + 4 q^{17} - 4 q^{19} - 17 q^{21} + 6 q^{23} + 3 q^{25} - 13 q^{27} + 2 q^{29} - 14 q^{31} - q^{35} + 4 q^{37} + 4 q^{39} + 9 q^{41} - 7 q^{43} - 2 q^{45} + 15 q^{47} + 18 q^{49} + 20 q^{51} - 6 q^{53} - 14 q^{57} - 10 q^{59} + 3 q^{61} + 12 q^{63} - 6 q^{65} - 19 q^{67} - 8 q^{69} - 6 q^{71} - 12 q^{73} - q^{75} - 2 q^{79} + 3 q^{81} - 18 q^{83} - 4 q^{85} - 10 q^{87} + 11 q^{89} - 20 q^{91} + 20 q^{93} + 4 q^{95} - 2 q^{97}+O(q^{100}) \) 3 * q - q^3 - 3 * q^5 + q^7 + 2 * q^9 + 6 * q^13 + q^15 + 4 * q^17 - 4 * q^19 - 17 * q^21 + 6 * q^23 + 3 * q^25 - 13 * q^27 + 2 * q^29 - 14 * q^31 - q^35 + 4 * q^37 + 4 * q^39 + 9 * q^41 - 7 * q^43 - 2 * q^45 + 15 * q^47 + 18 * q^49 + 20 * q^51 - 6 * q^53 - 14 * q^57 - 10 * q^59 + 3 * q^61 + 12 * q^63 - 6 * q^65 - 19 * q^67 - 8 * q^69 - 6 * q^71 - 12 * q^73 - q^75 - 2 * q^79 + 3 * q^81 - 18 * q^83 - 4 * q^85 - 10 * q^87 + 11 * q^89 - 20 * q^91 + 20 * q^93 + 4 * q^95 - 2 * q^97

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